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December 15

Euclidean plane?

Please tell me, is the Euclidean plane the concept of two dimensional space only, or is it the concept of 2D space + something else? ~ R.T.G 07:11, 15 December 2019 (UTC)

"Plane" specifies that it's two-dimensional. --142.112.159.101 (talk) 07:47, 15 December 2019 (UTC)

Yes it's definitely a 2D plane on which to do graphs and plots and stuff, however, if you search for sources "Euclidean plane" specifically... it no longer seems to be just the plane. One catch phrase seems to be, "it satisfies the axioms (Π'A1), (Π'A2), and (Π'A3)", explanations as to what that means are not included... ~ R.T.G 09:38, 15 December 2019 (UTC)

Why don’t you try to include enough information in your question so that others have some dim hope of understanding what you’re asking about. Right now answering appears to require being able to read your mind. —JBL (talk) 13:53, 15 December 2019 (UTC)

Pretty sure what the OP is referring to is [1], the page on sciencedirect.com. The page is cryptic and it's apparent purpose is to sell books rather than educate. I'd suggest trying a different website (like Wikipedia). It's pointless to spend time trying to decipher a confusing or poorly written text when there are so many others to choose from at this level. --RDBury (talk) 14:17, 15 December 2019 (UTC)

A Euclidean plane is a two dimensional area for plotting maths in. Is there something else specific about it that makes it a Euclidean plane, rather than just a plane used for geometry?

I'm looking for someone who can not only use a Euclidean plane, but describe it before and without, using math terms or figures, to you know, for like, someone who doesn't already know what it is, no really, they don't know what it is, but I want to explain it to them. No, they aren't stupid. It's me. I'm stupid. I can only explain things without math terms and figures. No, it's discriminatory to abuse me. Let's see, what other info was there? One of my favourite quotes from the guides that I am sure is gone now used to say, something like, "Try to write the article as though the reader has a perfect understanding of English, but has never heard of the subject before."

Don't worry, if you are just a simple math professor and this is beyond you... that's okay! That just means you are normal! ~ R.T.G 16:49, 15 December 2019 (UTC)

If you actually have a question you want answered, I recommend you devote some energy to communicating the question clearly -- performative rambling is not a good substitute. --JBL (talk) 17:10, 15 December 2019 (UTC)

The question is obvious and simple. Answer it, improve it, or get out the way? I'm not seeking approval. You are berating me for amusement. I've showed my sense of humour. There is no need to test me for patience. Thanks anyway o/ ~ R.T.G 18:31, 15 December 2019 (UTC)

I am telling you (again) that you have not articulated a question, at least not one with sufficient context for anyone else to know what might constitute an answer that would satisfy you. If you want a question answered, you should ask it clearly and concisely, with appropriate context. If you just want to jerk off, do it in private. --JBL (talk) 21:17, 15 December 2019 (UTC)

I am really sorry to inform you you failed. The properties of Euclidean plane appeared very interesting to me some time ago, so now I tried to follow this thread - alas, could not find a sense of humor in it. And not only a sense of humor, but actually little sense at all. What a pity, it could have been an interesting talk... --CiaPan (talk) 21:34, 15 December 2019 (UTC)

"A Euclidean plane is a two dimensional area for plotting maths in. Is there something else specific about it that makes it a Euclidean plane, rather than just a plane used for geometry?"

"A Euclidean plane is a two dimensional area for plotting maths in. Is there something else specific about it that makes it a Euclidean plane, rather than just a plane used for geometry?"

"A Euclidean plane is a two dimensional area for plotting maths in. Is there something else specific about it that makes it a Euclidean plane, rather than just a plane used for geometry?"

The original question:

"Please tell me, is the Euclidean plane the concept of two dimensional space only, or is it the concept of 2D space + something else?"

"Please tell me, is the Euclidean plane the concept of two dimensional space only, or is it the concept of 2D space + something else?"

"Please tell me, is the Euclidean plane the concept of two dimensional space only, or is it the concept of 2D space + something else?"

The original question consisted of "is it or isn't it". I'm not looking for help reading "science direct". I have found something simple which is not explained very well either on or off the site, across the board. People who cannot see a question and are more interest in discussing contributors than even discussing the content let alone attempting to answer it need not apply. A fool could understand this question. Answer it, or go and look at something else. There is no need for a tirade here. I wouldn't support closing the reference desks, but I might support a witch hunt because the way to stop a major fire is to remove the fuel. There is no need for anyone to respond here who isn't trying to answer this simple question. ~ R.T.G 05:31, 16 December 2019 (UTC)

I guess the simplest answer AFAIK, if not a totally precise one, is that what distinguishes the Euclidean plane from a general 2D vector space is that it is over the real numbers plus the notion of length and angle.

In more detail: you can think of the Euclidean plane as just R² (the set of all ordered pairs of real numbers, interpreted as coordinates like (0,0) or (4,3) and so on), equipped with the usual dot product to define lengths and angles. As stated at Euclidean space, every n-dimensional Euclidean space behaves exactly like (i.e. is isomorphic to) Rⁿ with the dot product, and you can make that explicit by picking an origin and drawing axes at right angles marked at unit length (i.e. picking an orthonormal basis). My apologies if I have made some inaccuracies in attempting to simplify this and leave the precise terms to parentheses... Double sharp (talk) 05:56, 16 December 2019 (UTC)

To simplify even further, the Euclidean plane is a plane in which the distance between two points is defined to be the Euclidean distance. There are many other ways to define the distance between two points, and Metric (mathematics) and Metric space contain further information.--Wikimedes (talk) 07:25, 16 December 2019 (UTC)

December 16

Proving the isoperimetric inequality with Lagrange multipliers applied to calculus of variations

I'm having a little bit of a conundrum here.

I am formulating the problem as maximizing $\int _{a}^{b}-xy'\ dt$ subject to $\int _{a}^{b}{\sqrt {x'^{2}+y'^{2}}}dt=K$. If I take the functional derivative of the inside of each integral, multiply the right hand side's functional derivative by a Lagrange multiplier, equate components, and divide the equations, I end up with a tautology. More explicitly, I have $(y',-x')=-{\frac {\lambda }{{\sqrt {x'^{2}+y'^{2}}}^{3}}}(x''(x'^{2}+y'^{2})-x'x'x''-x'y''y',y''(x'^{2}+y'^{2})-y'x'x''-y'y''y')$ which gets simplified to $-y'/x'={\frac {x''y'^{2}-x'y'y''}{y''x'^{2}-y'x'x''}}$, which is satisfied for all x and y such that the numerator and denominator aren't zero. This leads me to think that one must instead look at where they are zero, which occurs when $y''x'=y'x''$. This is satisfied only in the case $\ln(y')=\ln(x')+C$ which, however, does not exclude an ellipse.--Jasper Deng (talk) 03:49, 16 December 2019 (UTC)